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Yang-Mills fields on cyclindrical manifolds and holomorphic bundles II

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We give complex holomorphic descriptions of Yang-Mills instantons on tubular four manifolds with nontrivial cicle bundles over Riemann surfaces as section.

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References

  1. Bando, S.: Einstein-Hermitian metrics on non-compact Kaehle manifols. Preprint

  2. Biquard, O.: Fibre paraboliques Stables et Connexions Singulieres Plates. Bull. Soc. Math. France119, 231–257 (1991)

    Google Scholar 

  3. Buchdahl, N.P.: Hermitian-Einstein Connection and Stable Vector Bundles Over Compact Complex Surfaces. Math. Ann.280, 625–648 (1988)

    Google Scholar 

  4. Donaldson, S.K.: Anti self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles. Proc. London Math. Soc.50, 1–26 (1985)

    Google Scholar 

  5. Donaldson, S.K. Furuta, M. and Kotshick, D.: Floer homology groups in Yang-Mills theory. In preparation

  6. Fukaya, K.: Floer homology for oriented homology 3-spheres. Advanced Studies in Pure Mathematics20, Tokyo Konokuniya Company Ltd.,1992, pp. 1–92

  7. Furuta, M. and Steer, B.: Seifert Fibered Homology 3-spheres and the Yang-Mills Equations. Advances in Mathematics96, No. 1 38–102 (1992)

    Google Scholar 

  8. Guo, G.Y.: Yang-Mills fields on cylindrical manifolds and Holomorphic bundles I, Commun. Math. Phys.

  9. Guo, G.Y.: Thesis, Oxford

  10. Hamilton, R.S.: Harmonic maps of manifolds with boundary. LNM471, Berlin: Springer, 1982

    Google Scholar 

  11. Hamilton, R.S.: Three manifolds with positive Rici curvature. J. Diff. Geom.17, 253–306 (1982)

    Google Scholar 

  12. Kobayashi, S.: Differential geometry of complex vector bundles. Publ. Math. Soc. Japan, Iwanami Shoten and Princeton Univ., 1987

  13. Kroheimer, P. and Mrowka, T.: Gauge theory for embedded surfaces. I. Topology32, No. 4, 773–826; (1993) II, Topology34 37–97 (1995)

    Google Scholar 

  14. Metha, V.B. and Seshadri, C.S.: Moduli of vector bundles on curves with parabolic structures. Math. Ann.248, 205–239 (1980)

    Google Scholar 

  15. Narasimhan, M.S. and Seshadri, C.S.: Stable and unitary bundles on a compact Riemann surface. Ann. of Math.82, 540–564 (1965)

    Google Scholar 

  16. Simpson, C.T.: Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization. J. Amer. Math. Soc.1, 867–918 (1988)

    Google Scholar 

  17. Taubes, C.H.:L 2-moduli spaces on 4-manifolds with cylindrical ends. International Press, Hong Kong, 1994

    Google Scholar 

  18. Uhlenbeck, K.: Removable singularities in Yang-Mills fields. Commun. Math. Phys.83, 11–29 (1982)

    Google Scholar 

  19. Uhlenbeck, K.: Connections withL p bounds on curvature. Commun. Math. Phys.83, 31–42 (1982)

    Google Scholar 

  20. Uhlenbeck, K., and Yau, S.-T.: On the existence of Hernitian-Yang-Mills connections in stable vector bundles. Commun. Pure and Appl. Math.39-S, 257–293 (1986)

    Google Scholar 

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Communicated by S.-T. Yau

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Guo, GY. Yang-Mills fields on cyclindrical manifolds and holomorphic bundles II. Commun.Math. Phys. 179, 777–788 (1996). https://doi.org/10.1007/BF02100107

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  • DOI: https://doi.org/10.1007/BF02100107

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